Journal of Combinatorial Theory Series B
Distance-hereditary graphs, Steiner trees, and connected domination
SIAM Journal on Computing
On hypergraph acyclicity and graph chordality
Information Processing Letters
Discrete Applied Mathematics - Computational combinatiorics
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
Efficient Parallel Algorithms for Chordal Graphs
SIAM Journal on Computing
On the Desirability of Acyclic Database Schemes
Journal of the ACM (JACM)
Degrees of acyclicity for hypergraphs and relational database schemes
Journal of the ACM (JACM)
A linear time algorithm for minimum fill-in and treewidth for distance hereditary graphs
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
A simple paradigm for graph recognition: application to cographs and distance hereditary graphs
Theoretical Computer Science
Domination in distance-hereditary graphs
Discrete Applied Mathematics
Dynamic Programming on Distance-Hereditary Graphs
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
Centers and medians of distance-hereditary graphs
Discrete Mathematics
The Hamiltonian problem on distance-hereditary graphs
Discrete Applied Mathematics
Linear-time algorithms for the Hamiltonian problems on distance-hereditary graphs
Theoretical Computer Science
Longest Path Problems on Ptolemaic Graphs
IEICE - Transactions on Information and Systems
A new approach to graph recognition and applications to distance-hereditary graphs
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Lexicographic breadth first search – a survey
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Independent domination in chordal graphs
Operations Research Letters
Hi-index | 0.04 |
Ptolemaic graphs are those satisfying the Ptolemaic inequality for any four vertices. The graph class coincides with the intersection of chordal graphs and distance hereditary graphs. It can also be seen as a natural generalization of block graphs (and hence trees). In this paper, we first state a laminar structure of cliques, which leads to its canonical tree representation. This result is a translation of @c-acyclicity which appears in the context of relational database schemes. The tree representation gives a simple intersection model of ptolemaic graphs, and it is constructed in linear time from a perfect elimination ordering obtained by the lexicographic breadth first search. Hence the recognition and the graph isomorphism for ptolemaic graphs can be solved in linear time. Using the tree representation, we also give an efficient algorithm for the Hamiltonian cycle problem.